Question

10 and 11 please

LSM 5 Part C. Suppose that you are walking on a straight line. You start at position Xo =0, and only walk in the positive direction. Your positions after taking the ith step is denoted by X,. For each step, your step size, denoted by S, feet. Assume that sizes of different steps are m 8. (10 credits) Let Xy be your position after taking N steps where N is a given = X,-X,-, is a random variable uniformly distributed between 1 foot and 2 constant. Obtain EXy] and VarX 9. (10 credits) Use Chebyshev's inequality to obtain an upper bound to Now assume that in each step, you also make a random decision on the direction of your step. With a probability of 0.5, you will take a step in the positive direction; and with a probability of 0.5, you will take a step in the negative direction. Each step size is still random and uniformly distributed between 1 foot and 2 feet. Suppose that your direction decisions are mutually independent and also independent from everything else. 10. (10 credits) Let Xy be your position after taking N steps where N is a given constant. Obtain E[X] and Var[x 11. (10 credits) For large N, use the Central Limit Theorem to approximate YN]. Please express your result using the Q( ) function. PIX,-E[XN]

Answer 1

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